monetary exit strategy and fiscal spillovers · monetary exit strategy and fiscal spillovers...

Monetary Exit Strategy and Fiscal Spillovers

Jan Libich, Dat T. Nguyen, and Petr Stehlík

Supported by the Australian Research Council (DP0879638)

This Version: April 2012

Jan Libich, Dat T. Nguyen, and Petr Stehlík (Supported by the Australian Research Council (DP0879638))Monetary Exit and Fiscal Spillovers This Version: April 2012 1 / 42

The aftermath of a major contraction (think 2010-11): two types ofconcerns in regards to monetary policy outcomes

the short-term possibility of deflation caused by a prolonged slump(Krugman)excessively high inflation in the longer-term caused by politicalpressure to monetize the debt (Taylor)

Show of hands: In the United States, which concern did YOU findmore relevant in 2010/11?

We model strategic monetary-fiscal interactions jointly over bothhorizons

Perhaps surprisingly, we find that the probabilities of short-termdeflation and of long-term high inflation are positively related.

the short-term possibility of deflation caused by a prolonged slump(Krugman)

excessively high inflation in the longer-term caused by politicalpressure to monetize the debt (Taylor)

You May Be Thinking...

In the era of independent central banks, are there anyfiscal-monetary interactions to even talk about?

Background: Alarming Debt Projections

Let’s focus on the future rather than the current debt crisis in the EU.Below are projections of the public debt to GDP ratio in the U.S. using theCongressional Budget Offi ce data (from Leeper, 2010)

Figure:Jan Libich, Dat T. Nguyen, and Petr Stehlík (Supported by the Australian Research Council (DP0879638))Monetary Exit and Fiscal Spillovers This Version: April 2012 4 / 42

From IMF (2011) About the U.S.’s Intertemporal FiscalPosition

‘We find that, under our baseline scenario, a fullelimination of the fiscal and generational imbalanceswould require all taxes to go up and all transfers to becut immediately and permanently by 35 percent. A delayin the adjustment makes it more costly.’

It is Not Just the United States, and Not Just the GFC

The net present value of the impact of aging-related spending on fiscaldeficit (in percent of GDP): from IMF (2009).

One of the Main Driving Forces: Aging Populations

Old-age dependency ratios (population 65+ to population 15-64, UN data,2011-40 forecast)

Total Dependency Ratios (population 0-14 & 65+ to15-64)

‘Interesting’implications for capital and labour markets

Figure:

Pensioner per Worker Ratios in 2000: Bongaarts (2004)

Let’s Consider the Fiscal Implications: Expenditure onPensions and Healthcare by Age

From the IMF (2011) for the United States

0 10 20 30 40 50 60 70 80 90 100

Social Security

0 10 20 30 40 50 60 70 80 90 100

Medicare

MaleFemale

0 10 20 30 40 50 60 70 80 90 100

Medicaid

0 10 20 30 40 50 60 70 80 90 100

Unemployment Compensation

Figure:

Let’s Consider the Fiscal Implications: Tax Revenues byAge

From the IMF (2011) for the United States

0 10 20 30 40 50 60 70 80 90 100

Individual Income Taxes

0 10 20 30 40 50 60 70 80 90 100

Payroll Taxes

0 10 20 30 40 50 60 70 80 90 100

Capital Income Taxes

0 10 20 30 40 50 60 70 80 90 100

Excise Taxes

Figure:

So What...?

Should Central BankersCare

About All This?

Summary: Objectives

We focus on the strategic aspect of the monetary-fiscal interactions:absent in standard models. Why?

U.S. debt ceiling negotiations, ECB’s change of view on QE etc

Due to the looming fiscal gap, the government and the central bankhave different objectives

Therefore, they prefer a different policy stance, both in the SR and LR

Both policymakers act under incomplete information. Withprobability p ‘Downturn’scenario, with probability (1− p) ‘Normaltimes’scenario (think of the U.S. in 2010-11).

Summary: Objectives

Actions and Payoffs

To focus on the strategic interactions we analyze the policyinteractions as 2× 2 gamesBoth policymakers’decide about their policy stance: Active (tight M,easy F ) or Passive (easy M, tight F ).

FPassive Active

M Active a,w b, xPassive c , y d , z

Normal Times (probability 1− p)

FP ′ A′

M A′ a′,w ′ b′, x ′

P ′ c ′, y ′ d ′, z ′

Downturn (prob. p)

Leeper’s policy regimes exogenous: we endogenize the active/passivepolicy choice

Downturn: Battle of the Sexes

The paper shows that such game can be derived from a simple modelunder realistic assumptions (reflecting the 2010-11 situation)

FPassive Active

M Activedeflation−10,−10

recovery3, 2

Passiverecovery2, 3

over-stimulating1, 1

Substitutability of M and F measures: between mid-November 2010and end-March 2011 U.S. Treasury issued $589 billion in extralong-term debt (of which the Fed bought 87%) - undermining QEBernanke (2011): ‘it’s desirable that we take strong action to lowerour budget deficits over the longer term.... [but] in light of theweakness of the recovery, it would be best not to have sudden andsharp fiscal consolidation in the near term.’

FPassive Active

recovery3, 2

Passiverecovery2, 3

Substitutability of M and F measures: between mid-November 2010and end-March 2011 U.S. Treasury issued $589 billion in extralong-term debt (of which the Fed bought 87%) - undermining QE

Bernanke (2011): ‘it’s desirable that we take strong action to lowerour budget deficits over the longer term.... [but] in light of theweakness of the recovery, it would be best not to have sudden andsharp fiscal consolidation in the near term.’

FPassive Active

recovery3, 2

Passiverecovery2, 3

Substitutability of M and F measures: between mid-November 2010and end-March 2011 U.S. Treasury issued $589 billion in extralong-term debt (of which the Fed bought 87%) - undermining QEBernanke (2011): ‘it’s desirable that we take strong action to lowerour budget deficits over the longer term.... [but] in light of theweakness of the recovery, it would be best not to have sudden andsharp fiscal consolidation in the near term.’

Normal Times: Game of Chicken

M / F Passive Active

ActiveRicardian3, 2

explosive (tug-of-war)0, 0

Passivetug-of-war0, 0

monetization (spillovers)2, 3

Monetization [unpleasant monetarist arithmetic ala Sargent andWallace (1981)] or the Fiscal Theory of the Price Level [ala Leeper(1991)

In both scenarios: a coordination problem (avoiding the inferiormixed Nash), and a policy conflict (ensuring the preferred pureNash).These features present in many diverse interaction papers: E.g. Adamand Billi (2008), Branch, et al. (2008), Benhabib and Eusepi (2005), Dixit and

Lambertini (2003), Barnett (2001), Blake and Weale (1998), Nordhaus (1994), Sims

(1994), Woodford (1994), Leeper (1991), Petit (1989), or Alesina and Tabellini (1987).

ActiveRicardian3, 2

Monetization [unpleasant monetarist arithmetic ala Sargent andWallace (1981)] or the Fiscal Theory of the Price Level [ala Leeper(1991)In both scenarios: a coordination problem (avoiding the inferiormixed Nash), and a policy conflict (ensuring the preferred pureNash).

These features present in many diverse interaction papers: E.g. Adamand Billi (2008), Branch, et al. (2008), Benhabib and Eusepi (2005), Dixit and

ActiveRicardian3, 2

Monetization [unpleasant monetarist arithmetic ala Sargent andWallace (1981)] or the Fiscal Theory of the Price Level [ala Leeper(1991)In both scenarios: a coordination problem (avoiding the inferiormixed Nash), and a policy conflict (ensuring the preferred pureNash).These features present in many diverse interaction papers: E.g. Adamand Billi (2008), Branch, et al. (2008), Benhabib and Eusepi (2005), Dixit and

Estimated Regimes: USA (Leeper and Davig, 2010)

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

AM,PF − RicardianAM,AF − ExplosivePM,PF − IndeterminacyPM,AF − Fiscal Theory

Summary: Game Theoretic Framework

To incorporate institutional features our game theoretic frameworkallows for stochastic revisions of the policy stance

generalizing the Stackelberg leadership concept from static to dynamic.let’s plot this timing in a diagram

Inability to change the policy stance is interpreted as long-termmonetary commitment and fiscal rigidity.

generalizing the Stackelberg leadership concept from static to dynamic.

let’s plot this timing in a diagram

Timing of Moves

Nature makes a move about (current and near future) economicconditions given probability p.

Observing the draw, the players move simultaneously at time t = 0.

One of the players, called reviser, can move again in time t ∈ [0, 1]with some ex-ante known positive probability, observing the initialplay of the opponent (unlike the leader)Payoffs accrue continuously over t ∈ [0, 1] .A dynamic version of the Stackelberg leadership conceptIn Basov, Libich and Stehlík (2011) both players are revisers

Timing of the Revision Opportunity: Examples

In contrast to the standard simultaneous move game

3rd (Calvo) case: annual budget vs FOMC’s meetings (absence of Mcommitment, otherwise reversed)

Figure: Three examples of timing: (truncated) normal, uniform, andbinomial distributions, and the corresponding CDFs.

Timing of the Revision Opportunity: Examples

In contrast to the standard simultaneous move game3rd (Calvo) case: annual budget vs FOMC’s meetings (absence of Mcommitment, otherwise reversed)

Figure: Three examples of timing: (truncated) normal, uniform, andbinomial distributions, and the corresponding CDFs.

Stochastic/Continuous Setup

Definition

The revision function

F (t) : [0, 1]→ [0, 1], where F (0) = 0, (1)

is an arbitrary non-decreasing function summarizing the timing of therevision. It is the cumulative distribution function (CDF) of theunderlying probability distribution, i.e. it expresses the probability that thereviser has had the opportunity to revise no later than time t.

Stochastic/Continuous Setup

Definition

The integral∫ 10 F (t)dt describes the reaction speed of the revisers. The

complementary CDF

(1− F (t))dt = 1−1∫0

F (t)dt, (2)

expresses the degree of rigidity of the reviser. Therefore,

1∫ 10 (1− F (t))dt

∈ [1,∞) (3)

is the degree of the leader’s relative rigidity.

Results under Responsible M and Ambitious F

Three equilibrium regions separated by thresholds TF and TM :F -dominance: no double-dip, but M exit unsuccessfulM-dominance: no double-dip, and M exit successfulregime-switching: double-dip possible, M exit uncertain (so we mayget deflation now and high inflation later)

the strength of leadership: F rigidity relative to M commitment(expands the standard cases: F -leadership, simultaneous move,M-leadership)

Figure: Which region is the most likely one?Jan Libich, Dat T. Nguyen, and Petr Stehlík (Supported by the Australian Research Council (DP0879638))Monetary Exit and Fiscal Spillovers This Version: April 2012 23 / 42

Intuition (under p=0)

Focus on the case F rigidity > M commitmentSolving backwards, F knows that through her own inaction she canforce the bank to act.But the initial waiting game can be a costly tug-of-warFor F to surely-win the game AF must be the unique best responsenot only to PM, but also to AM.

x∫ 1

0(1− RM (t))dt︸︷︷︸conflict

+ z∫ 1

0RM (t)dt︸︷︷︸

F victory

> w︸︷︷︸ .F surrender

1∫ 10 (1− RM (t))dt

> TM =(z − x)(z − w) .

The ‘victory’area below the CDF must be suffi ciently large relative tothe ‘conflict’area above the CDF.

The regime-switching Case

Analogously, for the M-dominance case the central bank must bewilling to fight F

The intermediate regime-switching case does not exist under staticcommitment, and therefore has not been discussed in the Sargentand Wallace (1981) and Leeper (1991) literature.One policy is still the leader, but insuffi ciently so to fully dominatethe game.

This may be a possible advantage in the long-term, but adisadvantage in the short-term.Policies are more likely to engage in a costly tug-of-war (a ‘waitinggame’, trying to induce the other to respond, leading to deflation)

Additional Insights (Relative to Static StackelbergLeadership)

The thresholds TF and TM are increasing in the leader’s conflictcosts relative to his victory gain - in downturn and normal timesweighted by the probability p

1∫ 10 (1− RM (t))dt

> TM =p (y ′ − w ′) + (1− p) (z − x)p (y ′ − x ′) + (1− p) (z − w) > 1.

The magnitudes of the variables differ across countries

implying an explanation for the observed differences in institutionaldesign of both policies (e.g. not all countries legislated a numericalinflation target).

Additional Insights

If the cost/gain in downturn exceeds that in normal times then TFand TM are increasing in p.This implies that certain degree of M commitment suffi cient innormal times may be insuffi cient in a post-crisis situationThe future will show whether the FED and others fall in this category

A legislated M commitment may therefore serve as a credibilityinsurance over the course of the business cycle.Good monetary policy design may induce fiscal policy to behaveoptimally, both in the short responses and long-term stance.

Our Institutional Indices

To (approximitely) assign countries to the three equilibrium regionswe need to quantify the M commitment

F rigidity ratio.

We therefore develop an index of both institutional variables based onestablished indices in the literature.F rigidity: average of eight components based on: (i) the F spaceconcept of Aizenman and Jinjarak (2011), (ii) the estimatedprobabilities of a given F space by Ostry el al. (2010), (iii) the Fspace, F path, and F governance of Augustine el al. (2011), and (iv)average F balances over 2000-11.M commitment: average of four components based on: (i) thepolitical transparency measure of Eijffi nger and Geraats (2006) ascalculated by Dincer and Eichengreen (2011), and (ii) the finalresponsibility measure of the central bank accountability index ofHaan et al. (1998) as updated by Sousa (2002), and (iii) the inflationfocus and central bank accountability measures of Fry et al. (2000).

F rigidity ratio.We therefore develop an index of both institutional variables based onestablished indices in the literature.

F rigidity: average of eight components based on: (i) the F spaceconcept of Aizenman and Jinjarak (2011), (ii) the estimatedprobabilities of a given F space by Ostry el al. (2010), (iii) the Fspace, F path, and F governance of Augustine el al. (2011), and (iv)average F balances over 2000-11.M commitment: average of four components based on: (i) thepolitical transparency measure of Eijffi nger and Geraats (2006) ascalculated by Dincer and Eichengreen (2011), and (ii) the finalresponsibility measure of the central bank accountability index ofHaan et al. (1998) as updated by Sousa (2002), and (iii) the inflationfocus and central bank accountability measures of Fry et al. (2000).

F rigidity ratio.We therefore develop an index of both institutional variables based onestablished indices in the literature.F rigidity: average of eight components based on: (i) the F spaceconcept of Aizenman and Jinjarak (2011), (ii) the estimatedprobabilities of a given F space by Ostry el al. (2010), (iii) the Fspace, F path, and F governance of Augustine el al. (2011), and (iv)average F balances over 2000-11.

M commitment: average of four components based on: (i) thepolitical transparency measure of Eijffi nger and Geraats (2006) ascalculated by Dincer and Eichengreen (2011), and (ii) the finalresponsibility measure of the central bank accountability index ofHaan et al. (1998) as updated by Sousa (2002), and (iii) the inflationfocus and central bank accountability measures of Fry et al. (2000).

F rigidity ratio.We therefore develop an index of both institutional variables based onestablished indices in the literature.F rigidity: average of eight components based on: (i) the F spaceconcept of Aizenman and Jinjarak (2011), (ii) the estimatedprobabilities of a given F space by Ostry el al. (2010), (iii) the Fspace, F path, and F governance of Augustine el al. (2011), and (iv)average F balances over 2000-11.M commitment: average of four components based on: (i) thepolitical transparency measure of Eijffi nger and Geraats (2006) ascalculated by Dincer and Eichengreen (2011), and (ii) the finalresponsibility measure of the central bank accountability index ofHaan et al. (1998) as updated by Sousa (2002), and (iii) the inflationfocus and central bank accountability measures of Fry et al. (2000).

Fiscal Rigidity Country Ranking

Figure: Relative fiscal rigidity scores.

The Monetary Commitment vs Fiscal Rigidity Space

Figure: The monetary commitment vs fiscal rigidity space.Jan Libich, Dat T. Nguyen, and Petr Stehlík (Supported by the Australian Research Council (DP0879638))Monetary Exit and Fiscal Spillovers This Version: April 2012 30 / 42

Equilibrium Regions

Figure: Relative monetary commitment to fiscal rigidity scores ratios.

while countries such as Australia and New Zealand seem safely in theM dominance region, countries such as the United States and Japanare likely in the F dominance or Regime switching regions.

a (much) higher probability of both short-term deflation andlong-term high inflation in the latter pair of countries.

Equilibrium Regions

Figure: Relative monetary commitment to fiscal rigidity scores ratios.

while countries such as Australia and New Zealand seem safely in theM dominance region, countries such as the United States and Japanare likely in the F dominance or Regime switching regions.

a (much) higher probability of both short-term deflation andlong-term high inflation in the latter pair of countries.

TVP-VAR with Sign Restrictions

1984198919941999

200448

1984198919941999200448

Figure: Impulse responses of the interest rate (vertical axis) to a debt-financedgovernment spending shock in Australia (left) and the U.S. (right), for details seeFranta, Libich and Stehlík (2012).

Government Debt in Inflation Targeting Countries

Figure: Evolution of the government debt to GDP ratio (in %, demeaned) in EITcountries (top) and non-EIT countries (bottom). The start of the shaded areaindicates the regime’s adoption. For details see Franta, Libich, and Stehlik (2012).

Government Debt in Non-targeters

Figure: Evolution of the government debt to GDP ratio (in %, demeaned) in EITcountries (top) and non-EIT countries (bottom). The start of the shaded areaindicates the regime’s adoption.

Extension: Monetary Union with Three Types ofGovernments

Ambitious FA, responsible FR and ultra-ambitious FU .The common (responsible) central bank’s payoff is a weighted averageof the payoffs obtained from interactions with each government typei ∈ {A,R,U} using the weights f i .Showing how responsible governments potentially improve theoutcomes, and ultra-ambitious governments make them worse.Coalition of the common CB and responsible governments against thecoalition of the (ultra-)ambitious ones. If f R < f R , where

f R =f U [p(b′ − a′) + (1− p)(a− b)]− [p(b′ − c ′) + (1− p)(a− d)]

[p(c ′ − d ′) + (1− p)(d − c)] .

then the former coalition never ‘surely-wins’, i.e. we may haveF -spillovers even if the common CB is infinitely stronglycommitted (so only two equilibrium regions).

Summary and Conclusions

Understanding strategic monetary-fiscal interactions is important inthe current situation of F stress.Our analysis can roughly be interpreted as examining the followingquestion: ‘Which policy, if any, will (be forced to) deal with theshort-term threat of a double-dip recession, and which with thelong-term fiscal imbalance?’Need to ‘institutionalize’good policy - legislate commitment devicesthat ensure the right incentives of the policymakers (a mixture ofindependence, transparency and accountability - in both policies)In many countries direct fiscal reform seems politically diffi cult, sodiscipline can sometimes be achieved indirectly through (legislated)long-term monetary commitment, which may both:

reduce the risk of a double-dip recession and deflation in theshort-term, and

facilitate the exit strategy of M policy, ie prevent F spillovers

Understanding strategic monetary-fiscal interactions is important inthe current situation of F stress.Our analysis can roughly be interpreted as examining the followingquestion: ‘Which policy, if any, will (be forced to) deal with theshort-term threat of a double-dip recession, and which with thelong-term fiscal imbalance?’Need to ‘institutionalize’good policy - legislate commitment devicesthat ensure the right incentives of the policymakers (a mixture ofindependence, transparency and accountability - in both policies)In many countries direct fiscal reform seems politically diffi cult, sodiscipline can sometimes be achieved indirectly through (legislated)long-term monetary commitment, which may both:

reduce the risk of a double-dip recession and deflation in theshort-term, andfacilitate the exit strategy of M policy, ie prevent F spillovers

A legislated numerical target = monetary ‘credibility insurance’overall phases of the business cycle.

In line with Mishkin (2010): ‘Providing a firm anchor for long-runinflation expectations would make the threat of deflation less likely.But a firm anchor would also give the Fed flexibility to respond to theweakness of the economy —because it would help ensure that anynew moves to quantitative easing would not be misinterpreted assignalling a shift in the central bank’s long-run inflation goal, makingan upward surge in inflation expectations less likely too.’Brash (2011): ‘I have not the slightest doubt that having legislationwhich requires government and central bank to formally agree, anddisclose to the public, the inflation rate which the central bank musttarget has a most useful role in creating strong incentives for goodfiscal policy.’

In line with Mishkin (2010): ‘Providing a firm anchor for long-runinflation expectations would make the threat of deflation less likely.But a firm anchor would also give the Fed flexibility to respond to theweakness of the economy —because it would help ensure that anynew moves to quantitative easing would not be misinterpreted assignalling a shift in the central bank’s long-run inflation goal, makingan upward surge in inflation expectations less likely too.’

Brash (2011): ‘I have not the slightest doubt that having legislationwhich requires government and central bank to formally agree, anddisclose to the public, the inflation rate which the central bank musttarget has a most useful role in creating strong incentives for goodfiscal policy.’

In line with Mishkin (2010): ‘Providing a firm anchor for long-runinflation expectations would make the threat of deflation less likely.But a firm anchor would also give the Fed flexibility to respond to theweakness of the economy —because it would help ensure that anynew moves to quantitative easing would not be misinterpreted assignalling a shift in the central bank’s long-run inflation goal, makingan upward surge in inflation expectations less likely too.’Brash (2011): ‘I have not the slightest doubt that having legislationwhich requires government and central bank to formally agree, anddisclose to the public, the inflation rate which the central bank musttarget has a most useful role in creating strong incentives for goodfiscal policy.’

More Views on Monetary-Fiscal Interactions, the Euro etc

Hour-long video interviews with academics and policymakers (Dr DonBrash, Prof Eric Leeper, Prof Andrew Hughes Hallett, Dr Stefan Auer...)

Figure: Evolution of the government debt to GDP ratio (in %, demeaned) in EITcountries (top) and non-EIT countries (bottom). The start of the shaded areaindicates the regime’s adoption.

A Sketch of Fiscal Stress

What can be done about it (other than default)?

B1 − λZ1 − T1P1

= R0B0.

(only temporary) Borrowing: growing debt B1 − B0 > 0.

Structural fiscal reform: reducing Z and/or increasing T to ensurethe required level of Z1 − T1 ≤ 0 - passive F policyReneging on promises: λ = 0 - passive F policyMonetization [ala Sargent and Wallace (1981)]/Fiscal Theory ofthe Price Level [ala Leeper (1991)]: increase in P1 - passive Mpolicy

B1 − λZ1 − T1P1

= R0B0.

(only temporary) Borrowing: growing debt B1 − B0 > 0.Structural fiscal reform: reducing Z and/or increasing T to ensurethe required level of Z1 − T1 ≤ 0 - passive F policy

Reneging on promises: λ = 0 - passive F policyMonetization [ala Sargent and Wallace (1981)]/Fiscal Theory ofthe Price Level [ala Leeper (1991)]: increase in P1 - passive Mpolicy

B1 − λZ1 − T1P1

= R0B0.

(only temporary) Borrowing: growing debt B1 − B0 > 0.Structural fiscal reform: reducing Z and/or increasing T to ensurethe required level of Z1 − T1 ≤ 0 - passive F policyReneging on promises: λ = 0 - passive F policy

Monetization [ala Sargent and Wallace (1981)]/Fiscal Theory ofthe Price Level [ala Leeper (1991)]: increase in P1 - passive Mpolicy

B1 − λZ1 − T1P1

= R0B0.

(only temporary) Borrowing: growing debt B1 − B0 > 0.Structural fiscal reform: reducing Z and/or increasing T to ensurethe required level of Z1 − T1 ≤ 0 - passive F policyReneging on promises: λ = 0 - passive F policyMonetization [ala Sargent and Wallace (1981)]/Fiscal Theory ofthe Price Level [ala Leeper (1991)]: increase in P1 - passive Mpolicy

Active/Passive Policies

Policymakers’preferences:

Ui = −φi (P1 − PT )2 −(B1P1− bT

)2− δi (1− λ)2, (4)

where i ∈ {M,F} and φM > δM ≥ 0 and δF > φF ≥ 0.

Definition

An active policy is such that it provides no adjustment at all to balancethe budget constraint (4). That is P1 = PT and λ = 1. In contrast, apassive policy is such that it provides the full adjustment necessary tobalance the budget constraint and keep stable real debt - independently ofthe other policy (ie assuming the other policy is active). Specifically, it isP∗1 (Z ,T ) > P

T and λ∗ = 0.

Active/Passive Policies

Policymakers’preferences:

Ui = −φi (P1 − PT )2 −(B1P1− bT

)2− δi (1− λ)2, (4)

where i ∈ {M,F} and φM > δM ≥ 0 and δF > φF ≥ 0.

Definition

An active policy is such that it provides no adjustment at all to balancethe budget constraint (4). That is P1 = PT and λ = 1. In contrast, apassive policy is such that it provides the full adjustment necessary tobalance the budget constraint and keep stable real debt - independently ofthe other policy (ie assuming the other policy is active). Specifically, it isP∗1 (Z ,T ) > P

T and λ∗ = 0.

Mapping and Outcomes

For illustration normalize:R0 = B0 = 1 = P1 = PT = T = 1 < Z = 3, which implies bT = 1and P∗1 = 2.

FPF (λ∗ = 0) AF (λ = 1)

M AM(P1 = PT = 1

) Stable real debtB1P1= 1

1 = bT

Stable nominal debt

Rising real debtB1P1= 3

1 > bT

Rising nominal debt

PM (P∗1 = 2)Falling real debtB1P1= 1

2 < bT

Stable nominal debt

Stable real debtB1P1= 2

2 = bT

Rising nominal debt

Normal Times (probability 1-p)

FPF AF

M AM −δM ,−δF −4,−4PM −φM − 1

4 − δM ,−φF − 14 − δF −φM ,−φF

Normal Times

Naturally, in normal times assuming max {φM , δF } < 4, we get theGame of chicken:

a > d > max {b, c} and z > w > max {x , y} .

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